Wooden oval turning

Hi, I've been watching YouTube again and wonder if there is a way to mimic the process of oval turning ( http://www.youtube.com/watch?v=cDq5oHVD294 )

The basic process being as follows:

Two pieces of the desired wood with a sacrificial piece of wood in the centre,

A revolved cut around the assembly,

Remove the sacrificial piece of wood from the centre,

Mate the two pieces of desired wood together (and possibly a final revolve cut on the stem)...

The basic assembly, revolved cut, and removal of the sacrificial piece, all work fine. The problem occurs when I try to mate the two desired pieces together...

How ever I try to mate the two desired pieces together, the revolved cut then does not work. I.E. the desired pieces pull together and the cut updates to that shape - thus not achieving the effect I am after

I believe what is happening is that the order places the rearrangement of the components before the revolved cut... I cannot re order this.

I know that I could do the parts separately and then do a final assembly, once they are all fully shaped... but I would like to replicate the process if at all possible.

Thanks for reading.

I've attached a basic model - I figured that I'd start small and see if it can work before I make anything pretty

SolidworksAssemblies